3. The acidity of soils is measured by a quantity called the pH, which may range

Question

3. The acidity of soils is measured by a quantity called the pH, which may range from 0 (high acidity) to 14 (high alkalinity). A soil scientist wants to measure the average pH for a large field by randomly selecting n core samples and measuring the pH in each sample. Although the population standard deviation is not known, the sample standard deviation is calculated for n = 40 samples as S-072. Find the approximate probability that the sample mean of the 40 pH measurements will be within 4 units of the true average pH for the field

Explanation / Answer

z value = +/- 0.4 , s = 0.72 , n =20
we need to find
P(-0.4/SE < z < 0.4/SE)
= P( -0.4 / ( 0.72 / sqrt(20)) < z < (0.4 / ( 0.72 / sqrt(20))
= P(-2.4845 < z < 2.4845) by using z standard table

P(z < 2.4845) - P(z < -2.4845) = 0.98686

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